Recognition removes major stumbling block to better relations between East African neighbours.
The Ethiopian government has belatedly announced it will "fully accept and implement" a peace agreement with Eritrea that was signed in 2000.
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The pair fought a 1998-2000 war over a disputed town that a boundary commission subsequently handed to Asmara but which Addis Ababa rejected.
Eritrea invaded, and tens of thousands died or were taken prisoner on both sides.
Eritrea had been a province of Ethiopia until a 1993 referendum established independence. Eritrean fighters had helped in the overthrow of Ethiopia's military dictatorship and fought a 30-year war of independence. The country's creation transformed Ethiopia into a landlocked country.
It also transformed Eritrea, as the former ELM guerillas formed a government that has ruled ever since, attracting criticism for poor human rights, a lack of democracy, or a free media.